On the motion of a body in thermal equilibrium immersed in a perfect gas
Department of Mechanical Engineering and Science
and Advanced Research Institute of Fluid Science and Engineering,
Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan. email@example.com
2 Dipartimento di Matematica, Università di Roma “La Sapienza", Piazzale A. Moro 2, 00185, Roma, Italy. firstname.lastname@example.org; email@example.com; firstname.lastname@example.org
Revised: 16 October 2007
We consider a body immersed in a perfect gas and moving under the action of a constant force. Body and gas are in thermal equilibrium. We assume a stochastic interaction body/medium: when a particle of the medium hits the body, it is absorbed and immediately re-emitted with a Maxwellian distribution. This system gives rise to a microscopic model of friction. We study the approach of the body velocity V(t) to the limiting velocity and prove that, under suitable smallness assumptions, the approach to equilibrium is where d is the dimension of the space, and C is a positive constant. This approach is not exponential, as typical in friction problems, and even slower than for the same problem with elastic collisions.
Mathematics Subject Classification: 76P05 / 82B40 / 82C40 / 35L45 / 35L50
Key words: Kinetic theory of gases / Boltzmann equation / free molecular gas / friction problem / approach to equilibrium.
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